An Algorithm for the Extraction of Tafel Slopes

The Tafel equation, which serves as a linearized representation
of the Butler–Volmer expression, permits the extraction of
fundamental parameters of electrochemical systems, such as exchange
current densities and Tafel slopes. However, the application of these
linear fitting procedures become problematic in the cases of experimental
data featuring nonlinearities in the Tafel (log­(J) – V) response. This is especially troubling
in low-overpotential regimes, where charge transfer kinetics generally
dominate electrode behavior (as opposed to diffusion-limited currents
at higher overpotentials) and linearization is expected to be most
applicable. As a response to this complication and the ad-hoc forms
of fitting that may arise from it, this report outlines a systematic
method for the determination of Tafel slopes through a rigorous, quantitative
framework. The algorithm’s performance is benchmarked using
electrochemical measurements of well-characterized reactions for water
splitting, hydrogen evolution, and dioxygen reduction at iridium and
platinum electrodes. As a final validation test, we show that the
exchange currents extracted through this automated fitting procedure,
used in conjunction with the Butler–Volmer model, are capable
of reproducing the original electrochemical data in kinetically controlled
regimes.